Uniform tail asymptotics for the stochastic present value of aggregate claims in the renewal risk model
Consider an insurer who is allowed to make risk-free and risky investments. The price process of the investment portfolio is described as a geometric Lévy process. We study the tail probability of the stochastic present value of future aggregate claims. When the claim-size distribution is of Pareto type, we obtain a simple asymptotic formula which holds uniformly for all time horizons. The same asymptotic formula holds for the finite-time and infinite-time ruin probabilities. Restricting our attention to the so-called constant investment strategy, we show how the insurer adjusts his investment portfolio to maximize the expected terminal wealth subject to a constraint on the ruin probability.
Year of publication: |
2010
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Authors: | Tang, Qihe ; Wang, Guojing ; Yuen, Kam C. |
Published in: |
Insurance: Mathematics and Economics. - Elsevier, ISSN 0167-6687. - Vol. 46.2010, 2, p. 362-370
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Publisher: |
Elsevier |
Keywords: | Asymptotics Constant investment strategy Levy process Portfolio optimization Regular variation Ruin probability Uniformity |
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